My boat is on the hard right now for a bottom job. The yard provides power in the form of a standard household 15A outlet with GFCI. Whenever I plug my boat into it, either the GFCI trips or my main AC breaker trips. At first I thought it was too much current so I shut everything down except the charger and turned the charger to 2A. No dice. If I turn off literally every circuit then the main breaker and GFCI remain on, but that's not very useful. I never have trouble with marina shore power. Thoughts?

When you turned everything off except the charger you said "no dice". You then turned off the charger and all was fine (I make this assumption since the charger was the only thing that was on when you said you literally turned off everything). Then your charger has a ground fault.

To verify this start with everything off, then turn on one circuit at a time turning off the first before you try the second and see when or if the GFCI trips.

You said that the main tripped? You can check that out as well by using a similar method. This time turn on the circuits one at a time as above only don't turn them off before proceeding. Note if you have an electric hot water tank it must have water in it or you will fry your HW element. Do you have an electric HW tank and if so does it have water?